Two bidders compete in a sealed-bid auction for a single indivisible object. For each bidder i, the valuation of the object is uniformly distributed on [0, 1]. The valuations of the two bidders are independent. Each bidder knows her own valuation, but not the valuation of the other bidder. The bidders simultaneously submit bids b c [0, ∞), and whoever submits the higher bid wins the object and pays bidder 1's bid. In case of a tie, each bidder wins the object with probability 1/2 and again the winner pays bidder 1's bid. Find a Nash equilibrium of this game in which neither bidder plays a weakly dominated strategy.
Two bidders compete in a sealed-bid auction for a single indivisible object. For each bidder i, the valuation of the object is uniformly distributed on [0, 1]. The valuations of the two bidders are independent. Each bidder knows her own valuation, but not the valuation of the other bidder. The bidders simultaneously submit bids b c [0, ∞), and whoever submits the higher bid wins the object and pays bidder 1's bid. In case of a tie, each bidder wins the object with probability 1/2 and again the winner pays bidder 1's bid. Find a Nash equilibrium of this game in which neither bidder plays a weakly dominated strategy.
Chapter1: Making Economics Decisions
Section: Chapter Questions
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![Two bidders compete in a sealed-bid auction for a single indivisible object. For each bidder i,
the valuation of the object is uniformly distributed on [0, 1]. The valuations of the two bidders
are independent. Each bidder knows her own valuation, but not the valuation of the other
bidder. The bidders simultaneously submit bids b C [0, ∞), and whoever submits the higher
bid wins the object and pays bidder 1's bid. In case of a tie, each bidder wins the object with
probability 1/2 and again the winner pays bidder 1's bid. Find a Nash equilibrium of this
game in which neither bidder plays a weakly dominated strategy.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa1ab2968-d288-4fd8-b87c-74963c459231%2F234ce8b9-8093-405a-b24b-8d23a7022a0d%2Fh0rem0n_processed.png&w=3840&q=75)
Transcribed Image Text:Two bidders compete in a sealed-bid auction for a single indivisible object. For each bidder i,
the valuation of the object is uniformly distributed on [0, 1]. The valuations of the two bidders
are independent. Each bidder knows her own valuation, but not the valuation of the other
bidder. The bidders simultaneously submit bids b C [0, ∞), and whoever submits the higher
bid wins the object and pays bidder 1's bid. In case of a tie, each bidder wins the object with
probability 1/2 and again the winner pays bidder 1's bid. Find a Nash equilibrium of this
game in which neither bidder plays a weakly dominated strategy.
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